Angular Velocity

Question

In the early stages of solar-system formation, an approximately spherical cloud of gas and dust (radius 10^15 m, mass 10^31 kg) gradually contracts to form a much smaller, denser disk of material (radius 10^13 m, thickness 10^11 m, mass unchanged). Find the ratio of the final angular velocity to the initial angular velocity. Assume there are no significant external torques during the contraction.

Answer 1

By the Law of Conservation of angular momentum

L initial = L final

mrw^2 = MRW^2

W/w = sqrt [mr/(MR)]

Substitute and solve.